Most 3×3×3 Rubik's Cube solution guides use the same notation, created by David Singmaster, to communicate sequences of moves. This is generally referred to as "Cube notation" or in some literature "Singmaster notation" (or variations thereof). Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organized on a particular Cube.
Standard 3×3×3 notation
- F (Front): the side currently facing you
- B (Back): the side opposite the front
- U (Up): the side above or on top of the front side
- D (Down): the side opposite Up or on bottom
- L (Left): the side directly to the left of the front
- R (Right): the side directly to the right of the front
All letters mean to turn that face a quarter-turn clockwise as seen when looking at that face. (For instance, F'B does the same thing as turning the slice behind F a quarter-turn clockwise, then the entire cube a quarter-turn anticlockwise about the F-B axis.) When a prime symbol ['] follows a letter, it means to turn the face counter-clockwise a quarter-turn, while a letter without a prime symbol means to turn it a quarter-turn clockwise. Such a symbol is pronounced prime. A letter followed by a 2 (occasionally superscript) or by a second ["] means to turn the face a half-turn (the direction does not matter). Likewise, a number following a bracketed sequence means to do that sequence that number of times: for example, (F2 R2)3 = F2 R2 F2 R2 F2 R2, which does the two swaps UF-DF and UR-DR.
Cycles (exchanges of two or more pieces) are denoted by listing the pieces exchanged in order, with the facets ordered according to where they end up; thus the cycle (UF-DF) (UR-DR) above means that the UF edge goes to the DF position, with the facet that was at U going to D while the facet in F remains in F, and likewise for the other swap. The cycle UL-UF-UR below means that the UL edge goes to UF (and remains upright), the UF edge to UR, and the UR edge to UL. These are sometimes called straight cycles to distinguish them from twisted cycles. If a cubie flips or rotates as the result of a cycle, this is called a twisted cycle; for instance, the monoflip used in some Cube solutions, which flips the UR edge and several other edges not in the U layer, is denoted as UR+ or UR-. A monotwist of the ULF corner clockwise (U goes to F, F goes to L, L goes to U) is ULF+; anticlockwise is ULF-.
This notation can also be used on the Pocket Cube.
To extend this notation to the 3x3x3x3, for the fourth axis the letters A and K (ana and kata) could be used.
More advanced notation (slice moves, 4× and 5×)
It can also be used on the Revenge and the Professor, with additional notation. They not only have the F, B, L, R, U, D notation but also f, b, l, r, u, d. For example: (Rr)' l2 f'.
(A word of warning here. Some web pages use the lower-case letters to denote double-face turns, for instance f (on the 3×3×3) as the equivalent of B followed by a whole-Cube turn; or to denote whole-Cube turns. Be wary, and be sure to read any introduction the page offers.)
- f: the slice immediately behind F (and likewise the other five).
Note that "f" means to turn only that slice while keeping the F face still. If a turn of both the front slices is required, that is denoted by Ff or by F2 (not to be confused with F2 which is the traditional way of writing F2). Multi-slice turns are denoted using the notation in the previous sentence; for example, U3 means to turn all three U layers of a 5×5×5 (or larger) cube.
Sometimes the middle slices are used:
- M (Middle): the slice between L and R, as seen from L.
- E (Equator): the slice between U and D, as seen from D.
- S (Standing): the slice between F and B, as seen from F.
And of course, M', E' and S' have the same meanings but for anticlockwise turns. This notation also allows identification of the third slice in on V6 and V7 cubes.
Less often used moves include rotating the entire Cube or two-thirds of it. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of its axes.
- X or x: Rotate entire cube about the R face.
- X' or x': Rotate entire cube about L.
- Y or y: Rotate entire cube about U.
- Z or z: Rotate entire cube about F.
(This type of move is used infrequently in most solutions, to the extent that some solutions simply say "stop and turn the whole Cube upside-down" or something similar at the appropriate point.)
In speedcubing involving the 3×3×3, lowercase letters f, b, u, d, l, and r signify to move the first two layers of that face while keeping the remaining layer in place. This is of course equivalent to rotating the whole Cube in that direction, then rotating the opposite face back the same amount in the opposite direction, but is useful notation to describe certain triggers for speedcubing.
Even more advanced notation
Sometimes, face "slice moves" are denoted:
- Fs: turn F and B in parallel (FB')
- Bs: turn B and F in parallel (BF')
- Us: turn U and D in parallel (UD')
- Ds: turn D and U in parallel (DU')
- Ls: turn L and R in parallel (LR')
- Rs: turn R and L in parallel (RL')
These can be distinguished from the slice moves in the previous section by the use of the lower-case "s" suffix (slice) as opposed to the upper-case S (Standing slice).
There are also antislice moves:
- Fa or Ba: turn F and B in opposite directions (FB)
- Ua or Da: turn U and D in opposite directions (UD)
- La or Ra: turn L and R in opposite directions (LR)
This kind of notation can also be used for the slice moves in the previous section: M=Sl, M'=Sr, E=Sd, E'=Su, S=Sf, S'=Sb.
Finally, [P*Q] (P and Q can be any sequence of moves) is sometimes used to denote a conjugate (a sequence of the form P Q P'; P' meaning "do the sequence backwards", for instance, (R F2)'=F2 R'), and [P;Q] to denote a commutator (a sequence of the form P Q P' Q').
Some solution guides, including Ideal's official publication, The Ideal Solution, use slightly different conventions. Top and Bottom are used rather than Up and Down for the top and bottom faces, with Back being replaced by Posterior. + indicates clockwise rotation and - counterclockwise, with ++ representing a half-turn. However, alternative notations failed to catch on, and today the Singmaster scheme is used universally by those interested in the puzzle.
For example, the algorithm (or operator, or sequence) F2 U' R' L F2 R L' U' F2, which cycles UL-UF-UR without affecting any other part of the Cube, means:
- Turn the Front face 180 degrees
- Turn the Up face 90 degrees counterclockwise
- Turn the Right face 90 degrees counterclockwise
- Turn the Left face 90 degrees clockwise
- Turn the Front face 180 degrees
- Turn the Right face 90 degrees clockwise
- Turn the Left face 90 degrees counterclockwise
- Turn the Up face 90 degrees counterclockwise
- Finally, turn the front face 180 degrees.
For beginning students of the Cube, this notation can be daunting, and many solutions available online therefore incorporate animations that demonstrate the algorithms presented. For an example, see the video to the right, and this list of notations with pictures.
4×4×4 and larger Cubes use slightly different notation to incorporate the middle layers. Generally speaking, upper case letters (FBUDLR) refer to the outermost portions of the cube (called faces). Lower case letters (fbudlr) refer to the inner portions of the cube (called slices). Again Ideal breaks rank by describing their 4×4×4 solution in terms of layers (vertical slices that rotate about the Z-axis), tables (horizontal slices), and books (vertical slices that rotate about the X-axis).
Notations for other puzzles
Cuboids can use a version of cube notation. For sides where one of the dimensions is even and one is odd, they can only turn 180°, so a "2" is not needed and the letter alone can just be used.
With the official WCA pyraminx notation, the puzzle is held with a face facing you instead of a corner. There are 4 letters:
- L for the corner to the left
- R for the corner to the right
- U for the corner at the top
- B for the corner in the back
Capital letters indicate deep turns, lowercase letters indicate the trivial tips. The prime symbol works the same way as on the cube. Double moves are not necessary as they are equivalent to prime moves.
The same notation is used for the skewb. Hold the skewb with a corner pointing towards you.
The official WCA scramble notation for the megaminx uses only 6 moves:
- U and U' for rotating the top face 144° clockwise or counterclockwise respectively
- R++ and R-- for rotating the whole puzzle except the left face, 144° clockwise or counterclockwise respectively
- D++ and D-- for rotating the whole puzzle except the top face, 144° clockwise or counterclockwise respectively
Such a notation is only used for scrambling. In algorithms, a 3x3-like notation can be used for the top face and those adjacent to it. D is meaningless, but U, F, R and L can be used like on a 3x3. B needs to be split into BL (for the back face on the left) and BL (on the right). No prime or 2 means 72° clockwise, a 2 means 144°, and a prime means counterclockwise. Each turn has 4 forms (U, U', U2, U2').
Any notation for the Megaminx also works with any puzzle with the same cuts but shallower or deeper.
The Square-1 uses a notation different from other twisty puzzles. (A,B), where A and B are numbers, means to turn the top face A increments of 30° clockwise, and the bottom face B increments of 30° clockwise (negative numbers mean to turn counterclockwise). A slash (/) means to turn the entire left half of the puzzle 180°. In the newer WCA notation, the slash symbol is absent and every set of numbers is followed by a slash move.